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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.distribution;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    <a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.MathInternalError;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.random.RandomGenerator;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.random.RandomDataImpl;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
<FONT color="green">029</FONT>    <a name="line.29"></a>
<FONT color="green">030</FONT>    /**<a name="line.30"></a>
<FONT color="green">031</FONT>     * Base class for integer-valued discrete distributions.  Default<a name="line.31"></a>
<FONT color="green">032</FONT>     * implementations are provided for some of the methods that do not vary<a name="line.32"></a>
<FONT color="green">033</FONT>     * from distribution to distribution.<a name="line.33"></a>
<FONT color="green">034</FONT>     *<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Id: AbstractIntegerDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $<a name="line.35"></a>
<FONT color="green">036</FONT>     */<a name="line.36"></a>
<FONT color="green">037</FONT>    public abstract class AbstractIntegerDistribution<a name="line.37"></a>
<FONT color="green">038</FONT>    implements IntegerDistribution, Serializable {<a name="line.38"></a>
<FONT color="green">039</FONT>        /** Serializable version identifier */<a name="line.39"></a>
<FONT color="green">040</FONT>        private static final long serialVersionUID = -1146319659338487221L;<a name="line.40"></a>
<FONT color="green">041</FONT>    <a name="line.41"></a>
<FONT color="green">042</FONT>         /**<a name="line.42"></a>
<FONT color="green">043</FONT>          * RandomData instance used to generate samples from the distribution.<a name="line.43"></a>
<FONT color="green">044</FONT>          * @deprecated As of 3.1, to be removed in 4.0. Please use the<a name="line.44"></a>
<FONT color="green">045</FONT>          * {@link #random} instance variable instead.<a name="line.45"></a>
<FONT color="green">046</FONT>          */<a name="line.46"></a>
<FONT color="green">047</FONT>        @Deprecated<a name="line.47"></a>
<FONT color="green">048</FONT>        protected final RandomDataImpl randomData = new RandomDataImpl();<a name="line.48"></a>
<FONT color="green">049</FONT>    <a name="line.49"></a>
<FONT color="green">050</FONT>        /**<a name="line.50"></a>
<FONT color="green">051</FONT>         * RNG instance used to generate samples from the distribution.<a name="line.51"></a>
<FONT color="green">052</FONT>         * @since 3.1<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        protected final RandomGenerator random;<a name="line.54"></a>
<FONT color="green">055</FONT>    <a name="line.55"></a>
<FONT color="green">056</FONT>        /**<a name="line.56"></a>
<FONT color="green">057</FONT>         * @deprecated As of 3.1, to be removed in 4.0. Please use<a name="line.57"></a>
<FONT color="green">058</FONT>         * {@link #AbstractIntegerDistribution(RandomGenerator)} instead.<a name="line.58"></a>
<FONT color="green">059</FONT>         */<a name="line.59"></a>
<FONT color="green">060</FONT>        @Deprecated<a name="line.60"></a>
<FONT color="green">061</FONT>        protected AbstractIntegerDistribution() {<a name="line.61"></a>
<FONT color="green">062</FONT>            // Legacy users are only allowed to access the deprecated "randomData".<a name="line.62"></a>
<FONT color="green">063</FONT>            // New users are forbidden to use this constructor.<a name="line.63"></a>
<FONT color="green">064</FONT>            random = null;<a name="line.64"></a>
<FONT color="green">065</FONT>        }<a name="line.65"></a>
<FONT color="green">066</FONT>        /**<a name="line.66"></a>
<FONT color="green">067</FONT>         * @param rng Random number generator.<a name="line.67"></a>
<FONT color="green">068</FONT>         * @since 3.1<a name="line.68"></a>
<FONT color="green">069</FONT>         */<a name="line.69"></a>
<FONT color="green">070</FONT>        protected AbstractIntegerDistribution(RandomGenerator rng) {<a name="line.70"></a>
<FONT color="green">071</FONT>            random = rng;<a name="line.71"></a>
<FONT color="green">072</FONT>        }<a name="line.72"></a>
<FONT color="green">073</FONT>    <a name="line.73"></a>
<FONT color="green">074</FONT>        /**<a name="line.74"></a>
<FONT color="green">075</FONT>         * {@inheritDoc}<a name="line.75"></a>
<FONT color="green">076</FONT>         *<a name="line.76"></a>
<FONT color="green">077</FONT>         * The default implementation uses the identity<a name="line.77"></a>
<FONT color="green">078</FONT>         * &lt;p&gt;{@code P(x0 &lt; X &lt;= x1) = P(X &lt;= x1) - P(X &lt;= x0)}&lt;/p&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>         */<a name="line.79"></a>
<FONT color="green">080</FONT>        public double cumulativeProbability(int x0, int x1) throws NumberIsTooLargeException {<a name="line.80"></a>
<FONT color="green">081</FONT>            if (x1 &lt; x0) {<a name="line.81"></a>
<FONT color="green">082</FONT>                throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,<a name="line.82"></a>
<FONT color="green">083</FONT>                        x0, x1, true);<a name="line.83"></a>
<FONT color="green">084</FONT>            }<a name="line.84"></a>
<FONT color="green">085</FONT>            return cumulativeProbability(x1) - cumulativeProbability(x0);<a name="line.85"></a>
<FONT color="green">086</FONT>        }<a name="line.86"></a>
<FONT color="green">087</FONT>    <a name="line.87"></a>
<FONT color="green">088</FONT>        /**<a name="line.88"></a>
<FONT color="green">089</FONT>         * {@inheritDoc}<a name="line.89"></a>
<FONT color="green">090</FONT>         *<a name="line.90"></a>
<FONT color="green">091</FONT>         * The default implementation returns<a name="line.91"></a>
<FONT color="green">092</FONT>         * &lt;ul&gt;<a name="line.92"></a>
<FONT color="green">093</FONT>         * &lt;li&gt;{@link #getSupportLowerBound()} for {@code p = 0},&lt;/li&gt;<a name="line.93"></a>
<FONT color="green">094</FONT>         * &lt;li&gt;{@link #getSupportUpperBound()} for {@code p = 1}, and&lt;/li&gt;<a name="line.94"></a>
<FONT color="green">095</FONT>         * &lt;li&gt;{@link #solveInverseCumulativeProbability(double, int, int)} for<a name="line.95"></a>
<FONT color="green">096</FONT>         *     {@code 0 &lt; p &lt; 1}.&lt;/li&gt;<a name="line.96"></a>
<FONT color="green">097</FONT>         * &lt;/ul&gt;<a name="line.97"></a>
<FONT color="green">098</FONT>         */<a name="line.98"></a>
<FONT color="green">099</FONT>        public int inverseCumulativeProbability(final double p) throws OutOfRangeException {<a name="line.99"></a>
<FONT color="green">100</FONT>            if (p &lt; 0.0 || p &gt; 1.0) {<a name="line.100"></a>
<FONT color="green">101</FONT>                throw new OutOfRangeException(p, 0, 1);<a name="line.101"></a>
<FONT color="green">102</FONT>            }<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>            int lower = getSupportLowerBound();<a name="line.104"></a>
<FONT color="green">105</FONT>            if (p == 0.0) {<a name="line.105"></a>
<FONT color="green">106</FONT>                return lower;<a name="line.106"></a>
<FONT color="green">107</FONT>            }<a name="line.107"></a>
<FONT color="green">108</FONT>            if (lower == Integer.MIN_VALUE) {<a name="line.108"></a>
<FONT color="green">109</FONT>                if (checkedCumulativeProbability(lower) &gt;= p) {<a name="line.109"></a>
<FONT color="green">110</FONT>                    return lower;<a name="line.110"></a>
<FONT color="green">111</FONT>                }<a name="line.111"></a>
<FONT color="green">112</FONT>            } else {<a name="line.112"></a>
<FONT color="green">113</FONT>                lower -= 1; // this ensures cumulativeProbability(lower) &lt; p, which<a name="line.113"></a>
<FONT color="green">114</FONT>                            // is important for the solving step<a name="line.114"></a>
<FONT color="green">115</FONT>            }<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>            int upper = getSupportUpperBound();<a name="line.117"></a>
<FONT color="green">118</FONT>            if (p == 1.0) {<a name="line.118"></a>
<FONT color="green">119</FONT>                return upper;<a name="line.119"></a>
<FONT color="green">120</FONT>            }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>            // use the one-sided Chebyshev inequality to narrow the bracket<a name="line.122"></a>
<FONT color="green">123</FONT>            // cf. AbstractRealDistribution.inverseCumulativeProbability(double)<a name="line.123"></a>
<FONT color="green">124</FONT>            final double mu = getNumericalMean();<a name="line.124"></a>
<FONT color="green">125</FONT>            final double sigma = FastMath.sqrt(getNumericalVariance());<a name="line.125"></a>
<FONT color="green">126</FONT>            final boolean chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) ||<a name="line.126"></a>
<FONT color="green">127</FONT>                    Double.isInfinite(sigma) || Double.isNaN(sigma) || sigma == 0.0);<a name="line.127"></a>
<FONT color="green">128</FONT>            if (chebyshevApplies) {<a name="line.128"></a>
<FONT color="green">129</FONT>                double k = FastMath.sqrt((1.0 - p) / p);<a name="line.129"></a>
<FONT color="green">130</FONT>                double tmp = mu - k * sigma;<a name="line.130"></a>
<FONT color="green">131</FONT>                if (tmp &gt; lower) {<a name="line.131"></a>
<FONT color="green">132</FONT>                    lower = ((int) Math.ceil(tmp)) - 1;<a name="line.132"></a>
<FONT color="green">133</FONT>                }<a name="line.133"></a>
<FONT color="green">134</FONT>                k = 1.0 / k;<a name="line.134"></a>
<FONT color="green">135</FONT>                tmp = mu + k * sigma;<a name="line.135"></a>
<FONT color="green">136</FONT>                if (tmp &lt; upper) {<a name="line.136"></a>
<FONT color="green">137</FONT>                    upper = ((int) Math.ceil(tmp)) - 1;<a name="line.137"></a>
<FONT color="green">138</FONT>                }<a name="line.138"></a>
<FONT color="green">139</FONT>            }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>            return solveInverseCumulativeProbability(p, lower, upper);<a name="line.141"></a>
<FONT color="green">142</FONT>        }<a name="line.142"></a>
<FONT color="green">143</FONT>    <a name="line.143"></a>
<FONT color="green">144</FONT>        /**<a name="line.144"></a>
<FONT color="green">145</FONT>         * This is a utility function used by {@link<a name="line.145"></a>
<FONT color="green">146</FONT>         * #inverseCumulativeProbability(double)}. It assumes {@code 0 &lt; p &lt; 1} and<a name="line.146"></a>
<FONT color="green">147</FONT>         * that the inverse cumulative probability lies in the bracket {@code<a name="line.147"></a>
<FONT color="green">148</FONT>         * (lower, upper]}. The implementation does simple bisection to find the<a name="line.148"></a>
<FONT color="green">149</FONT>         * smallest {@code p}-quantile &lt;code&gt;inf{x in Z | P(X&lt;=x) &gt;= p}&lt;/code&gt;.<a name="line.149"></a>
<FONT color="green">150</FONT>         *<a name="line.150"></a>
<FONT color="green">151</FONT>         * @param p the cumulative probability<a name="line.151"></a>
<FONT color="green">152</FONT>         * @param lower a value satisfying {@code cumulativeProbability(lower) &lt; p}<a name="line.152"></a>
<FONT color="green">153</FONT>         * @param upper a value satisfying {@code p &lt;= cumulativeProbability(upper)}<a name="line.153"></a>
<FONT color="green">154</FONT>         * @return the smallest {@code p}-quantile of this distribution<a name="line.154"></a>
<FONT color="green">155</FONT>         */<a name="line.155"></a>
<FONT color="green">156</FONT>        protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {<a name="line.156"></a>
<FONT color="green">157</FONT>            while (lower + 1 &lt; upper) {<a name="line.157"></a>
<FONT color="green">158</FONT>                int xm = (lower + upper) / 2;<a name="line.158"></a>
<FONT color="green">159</FONT>                if (xm &lt; lower || xm &gt; upper) {<a name="line.159"></a>
<FONT color="green">160</FONT>                    /*<a name="line.160"></a>
<FONT color="green">161</FONT>                     * Overflow.<a name="line.161"></a>
<FONT color="green">162</FONT>                     * There will never be an overflow in both calculation methods<a name="line.162"></a>
<FONT color="green">163</FONT>                     * for xm at the same time<a name="line.163"></a>
<FONT color="green">164</FONT>                     */<a name="line.164"></a>
<FONT color="green">165</FONT>                    xm = lower + (upper - lower) / 2;<a name="line.165"></a>
<FONT color="green">166</FONT>                }<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>                double pm = checkedCumulativeProbability(xm);<a name="line.168"></a>
<FONT color="green">169</FONT>                if (pm &gt;= p) {<a name="line.169"></a>
<FONT color="green">170</FONT>                    upper = xm;<a name="line.170"></a>
<FONT color="green">171</FONT>                } else {<a name="line.171"></a>
<FONT color="green">172</FONT>                    lower = xm;<a name="line.172"></a>
<FONT color="green">173</FONT>                }<a name="line.173"></a>
<FONT color="green">174</FONT>            }<a name="line.174"></a>
<FONT color="green">175</FONT>            return upper;<a name="line.175"></a>
<FONT color="green">176</FONT>        }<a name="line.176"></a>
<FONT color="green">177</FONT>    <a name="line.177"></a>
<FONT color="green">178</FONT>        /** {@inheritDoc} */<a name="line.178"></a>
<FONT color="green">179</FONT>        public void reseedRandomGenerator(long seed) {<a name="line.179"></a>
<FONT color="green">180</FONT>            random.setSeed(seed);<a name="line.180"></a>
<FONT color="green">181</FONT>            randomData.reSeed(seed);<a name="line.181"></a>
<FONT color="green">182</FONT>        }<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>        /**<a name="line.184"></a>
<FONT color="green">185</FONT>         * {@inheritDoc}<a name="line.185"></a>
<FONT color="green">186</FONT>         *<a name="line.186"></a>
<FONT color="green">187</FONT>         * The default implementation uses the<a name="line.187"></a>
<FONT color="green">188</FONT>         * &lt;a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"&gt;<a name="line.188"></a>
<FONT color="green">189</FONT>         * inversion method&lt;/a&gt;.<a name="line.189"></a>
<FONT color="green">190</FONT>         */<a name="line.190"></a>
<FONT color="green">191</FONT>        public int sample() {<a name="line.191"></a>
<FONT color="green">192</FONT>            return inverseCumulativeProbability(random.nextDouble());<a name="line.192"></a>
<FONT color="green">193</FONT>        }<a name="line.193"></a>
<FONT color="green">194</FONT>    <a name="line.194"></a>
<FONT color="green">195</FONT>        /**<a name="line.195"></a>
<FONT color="green">196</FONT>         * {@inheritDoc}<a name="line.196"></a>
<FONT color="green">197</FONT>         *<a name="line.197"></a>
<FONT color="green">198</FONT>         * The default implementation generates the sample by calling<a name="line.198"></a>
<FONT color="green">199</FONT>         * {@link #sample()} in a loop.<a name="line.199"></a>
<FONT color="green">200</FONT>         */<a name="line.200"></a>
<FONT color="green">201</FONT>        public int[] sample(int sampleSize) {<a name="line.201"></a>
<FONT color="green">202</FONT>            if (sampleSize &lt;= 0) {<a name="line.202"></a>
<FONT color="green">203</FONT>                throw new NotStrictlyPositiveException(<a name="line.203"></a>
<FONT color="green">204</FONT>                        LocalizedFormats.NUMBER_OF_SAMPLES, sampleSize);<a name="line.204"></a>
<FONT color="green">205</FONT>            }<a name="line.205"></a>
<FONT color="green">206</FONT>            int[] out = new int[sampleSize];<a name="line.206"></a>
<FONT color="green">207</FONT>            for (int i = 0; i &lt; sampleSize; i++) {<a name="line.207"></a>
<FONT color="green">208</FONT>                out[i] = sample();<a name="line.208"></a>
<FONT color="green">209</FONT>            }<a name="line.209"></a>
<FONT color="green">210</FONT>            return out;<a name="line.210"></a>
<FONT color="green">211</FONT>        }<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>        /**<a name="line.213"></a>
<FONT color="green">214</FONT>         * Computes the cumulative probability function and checks for {@code NaN}<a name="line.214"></a>
<FONT color="green">215</FONT>         * values returned. Throws {@code MathInternalError} if the value is<a name="line.215"></a>
<FONT color="green">216</FONT>         * {@code NaN}. Rethrows any exception encountered evaluating the cumulative<a name="line.216"></a>
<FONT color="green">217</FONT>         * probability function. Throws {@code MathInternalError} if the cumulative<a name="line.217"></a>
<FONT color="green">218</FONT>         * probability function returns {@code NaN}.<a name="line.218"></a>
<FONT color="green">219</FONT>         *<a name="line.219"></a>
<FONT color="green">220</FONT>         * @param argument input value<a name="line.220"></a>
<FONT color="green">221</FONT>         * @return the cumulative probability<a name="line.221"></a>
<FONT color="green">222</FONT>         * @throws MathInternalError if the cumulative probability is {@code NaN}<a name="line.222"></a>
<FONT color="green">223</FONT>         */<a name="line.223"></a>
<FONT color="green">224</FONT>        private double checkedCumulativeProbability(int argument)<a name="line.224"></a>
<FONT color="green">225</FONT>            throws MathInternalError {<a name="line.225"></a>
<FONT color="green">226</FONT>            double result = Double.NaN;<a name="line.226"></a>
<FONT color="green">227</FONT>            result = cumulativeProbability(argument);<a name="line.227"></a>
<FONT color="green">228</FONT>            if (Double.isNaN(result)) {<a name="line.228"></a>
<FONT color="green">229</FONT>                throw new MathInternalError(LocalizedFormats<a name="line.229"></a>
<FONT color="green">230</FONT>                        .DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);<a name="line.230"></a>
<FONT color="green">231</FONT>            }<a name="line.231"></a>
<FONT color="green">232</FONT>            return result;<a name="line.232"></a>
<FONT color="green">233</FONT>        }<a name="line.233"></a>
<FONT color="green">234</FONT>    }<a name="line.234"></a>




























































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